Mark Thompson looks set to keep the reins at CNN in the near term as incoming owner David Ellison seeks stability at the cable network — but the possibility of Bari Weiss eventually gaining authority there remains alive, according to multiple reports.

Ellison is working on a deal to keep Thompson, CNN’s chief executive and editor in chief, in charge for “at least the next year,” the New York Times reported, citing people with knowledge of the talks.

The short-term arrangement comes after The Post reported Wednesday that Weiss had initially been promised CNN when she took over CBS News, but that Ellison subsequently concluded “her current role is more than she can handle,” according to a person with knowledge of the situation.

The Post also reported that Weiss remains in the Ellisons’ good graces.

A source close to the situation said that David’s father, Oracle co-founder Larry Ellison, “still loves Bari” and wants to keep her at the company, while another person said Paramount could eventually install a single executive over both CNN and CBS News.

One person told The Post that Paramount could eventually install a single executive over both CNN and CBS News, but said head honchos at the company currently “don’t want more headaches and crises.”

“This isn’t their top priority or their 20th priority,” the person said.

For the time being, Weiss is expected to remain focused on CBS News without editorial or operational oversight of CNN when Paramount’s acquisition of Warner Bros. Discovery closes, according to sources.

But that arrangement may not represent Ellison’s long-term vision for his news empire.

The Times reported that Weiss retains the support of the Ellison family and that her role “could eventually change” — leaving open the possibility that the CBS News editor-in-chief could ultimately gain responsibilities at CNN.

Weiss has not been permanently ruled out, despite Ellison cooling on the prospect of immediately handing her CNN after months of turmoil surrounding her overhaul of CBS News and “60 Minutes,” according to Status.

The Wall Street Journal reported on Wednesday that Ellison had asked Thompson to stay and that Weiss was not expected to have a CNN role when the Warner deal closes.

For Thompson, 69, even the immediate future remains subject to negotiations.

Status reported that talks over extending his contract, which expires in the spring, remain in their early stages. The Times cautioned that Thompson and Ellison could still fail to reach an agreement.

Thompson has made preserving his editorial authority a priority in the negotiations, according to the reporting.

He traveled to California this week and met privately with Ellison at Paramount on Thursday, according to Status.

News that Ellison wanted Thompson to remain triggered relief inside CNN after months of uncertainty about who would run the network under Paramount.

One CNN staffer texted Status, “Please tell me this is accurate,” while another described the mood after the news broke as “palpable” joy.

The arrangement also comes after CNN star Anderson Cooper reportedly told colleagues he did not want to work for Weiss.

Weiss, meanwhile, has presided over a contentious remake of CBS News, most dramatically at “60 Minutes,” where a series of firings and editorial disputes triggered fierce criticism from former correspondents.

Status reported that Ellison had previously envisioned giving Weiss editorial oversight of CNN but became less enthusiastic about doing so following the upheaval.

The Post has sought comment from CNN, CBS News and Paramount.